Solution of Fokker‐Planck‐Kolmogorov equation in stochastic modeling of fatigue crack propagation
作者:
Wen‐Fang Wu,
Tsan‐Hua Huang,
期刊:
Journal of the Chinese Institute of Engineers
(Taylor Available online 1990)
卷期:
Volume 13,
issue 1
页码: 25-33
ISSN:0253-3839
年代: 1990
DOI:10.1080/02533839.1990.9677227
出版商: Taylor & Francis Group
关键词: Markov process;Fokker‐Planck‐Kolmogorov equation;fatigue crack propagation;first‐passage problem
数据来源: Taylor
摘要:
Based on linear fracture mechanics concepts and random process theory, several stochastic models of fatigue crack propagation have been proposed in recent years. One of the models randomizes the fatigue crack propagation equation by employing a random pulse train and applying a stochastic average technique to treat the dynamic fatigue crack propagation as a Markov process. The probabilistic structure of a Markov diffusion process is governed by a Fokker‐Planck‐Kolmogorov equation. Therefore, in the present paper, the probability distribution of crack size at any given time and the probability distribution function of the random time at which a given crack size is reached are treated as solutions of the Fokker‐Planck‐Kolmogorov equation associated with the Markov process. Analytical solutions are found for these quantities and numerical examples are given. The results are compared with some experimentally obtained data.
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